Last visit was: 20 Nov 2025, 04:54 It is currently 20 Nov 2025, 04:54
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
EvaJager
User avatar
Joined: 22 Mar 2011
Last visit: 31 Aug 2016
Posts: 514
Own Kudos:
2,326
 [1]
Given Kudos: 43
WE:Science (Education)
Posts: 514
Kudos: 2,326
 [1]
What is my age (expressed as a positive integer)? Although 10 Oct 2012, 12:25
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

36% (03:27) correct 64% (02:26) wrong based on 62 sessions

History

Date
Time
Result
Not Attempted Yet
I know my age is no excuse for the silly mistakes I am making sometimes. I cannot change my age, so I should do something about the mistakes...
Contemplating my age, I just realized that the integer number that represents my age has some very nice properties :o)

What is my age (expressed as a positive integer)? Although not young anymore, my age is still a two digit integer.

(1) My age is the sum of two distinct perfect squares.
(2) My age can be written as the product of a two digit integer and the sum of its digits. The two digits are distinct and their sum is a perfect square.
ShowHide Answer
Official Answer
C
User avatar
geno5
User avatar
Joined: 05 Dec 2011
Last visit: 29 Mar 2022
Posts: 66
Own Kudos:
99
Given Kudos: 2
Location: Canada
Concentration: Accounting, Finance
GMAT Date: 09-08-2012
GPA: 3
Products:
My Reviews
Posts: 66
Kudos: 99
What is my age (expressed as a positive integer)? Although 10 Oct 2012, 14:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Evajager,

I got the right answer but I am abit unsure on statement 2. Could you solve the question. I understand if you waiting for others to post first.

I am abit unclear on this part of the statement (2) My age can be written as the product of a two digit integer and the sum of its digits.
avatar
aah123
avatar
Joined: 08 Oct 2012
Last visit: 29 Mar 2013
Posts: 17
Own Kudos:
2
Posts: 17
Kudos: 2
What is my age (expressed as a positive integer)? Although 10 Oct 2012, 14:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I am posting here for the first time as I joined GMAT club recently.

If we take statement (2) then according to that i took two digit integer as 13 and the sum of it's digits is 4( which is a perfect square) so the product of 13 and 4 = 52.

now according to statement first 16( which is a perfect square)+ 36( which is also a perfect square) = 52 which is the age in two digits.

so the answer is C
User avatar
EvaJager
User avatar
Joined: 22 Mar 2011
Last visit: 31 Aug 2016
Posts: 514
Own Kudos:
2,326
Given Kudos: 43
WE:Science (Education)
Posts: 514
Kudos: 2,326
What is my age (expressed as a positive integer)? Although 10 Oct 2012, 14:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
geno5
Evajager,

I got the right answer but I am abit unsure on statement 2. Could you solve the question. I understand if you waiting for others to post first.

I am abit unclear on this part of the statement (2) My age can be written as the product of a two digit integer and the sum of its digits.
Show more


You guys, just being too polite, don't want to reveal my age. Well, it seems that I have no choice, I have to do it...

(1) Obviously not sufficient. Too many options: 4 + 25 = 29, 9 + 25 = 34, 4 + 36 = 40... (wishful thinking)

(2) My age is (A + B)AB, where AB is a two digit number, A and B are distinct, and A + B is a perfect square.
Possible solutions: AB = 10, (1 + 0)*10 = 10.
4*13 =52 (4*31 = 124 > 100)
Next perfect square is 9. But any two digits with sum 9, when multiplied by 9, will give a number greater than 100. 9*18 is the smallest and already greater than 100.

So, we are left with two possibilities: 10 and 52.

(1) and (2) together: 10 = 1 + 9 and 52 = 16 + 36, both are sums of two perfect squares.
So, the answer should be E. If we take into account that I am an adult, then B should be the answer.

I cannot full you anymore...I am 52 years old.

Just a short summary of the properties of the number 52:
\(52 = 4*13\) \(,\,\,\,4=2^2\) and \(4 = 1 + 3.\)
\(52 = 16 + 36 = 4^2+6^2\), sum of two consecutive even squares.
\(13 = 4 + 9 = 2^2+3^2\), sum of two consecutive squares.

Can you find some more?

Next year is going to be 53. Prime number. Until now, I just found that \(53=6\cdot{9}-1=(2\cdot{3})\cdot{3^2}-1.\)
User avatar
EvaJager
User avatar
Joined: 22 Mar 2011
Last visit: 31 Aug 2016
Posts: 514
Own Kudos:
2,326
Given Kudos: 43
WE:Science (Education)
Posts: 514
Kudos: 2,326
What is my age (expressed as a positive integer)? Although 10 Oct 2012, 15:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
aah123
I am posting here for the first time as I joined GMAT club recently.

If we take statement (2) then according to that i took two digit integer as 13 and the sum of it's digits is 4( which is a perfect square) so the product of 13 and 4 = 52.

now according to statement first 16( which is a perfect square)+ 36( which is also a perfect square) = 52 which is the age in two digits.

so the answer is C
Show more

Welcome to the Club!
This is not a real GMAT test question, I was just trying to fool the club members...

I guess you didn't consider 10 as a possible solution for (2).
But you are right, I am 52. And as formulated, the answer to the question is either B or E, depending on whether we regard 10 as a possible solution or not.
avatar
aah123
avatar
Joined: 08 Oct 2012
Last visit: 29 Mar 2013
Posts: 17
Own Kudos:
2
Posts: 17
Kudos: 2
What is my age (expressed as a positive integer)? Although 10 Oct 2012, 16:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks Evajager,
Yes I did not consider 10, I don't know how come I counted only till 9.
So what's the answer then...is it (E) or (C).

I am just understanding how data sufficiency works, as my math concepts are good but this part is new to me.
User avatar
EvaJager
User avatar
Joined: 22 Mar 2011
Last visit: 31 Aug 2016
Posts: 514
Own Kudos:
2,326
Given Kudos: 43
WE:Science (Education)
Posts: 514
Kudos: 2,326
What is my age (expressed as a positive integer)? Although 11 Oct 2012, 02:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
aah123
Thanks Evajager,
Yes I did not consider 10, I don't know how come I counted only till 9.
So what's the answer then...is it (E) or (C).

I am just understanding how data sufficiency works, as my math concepts are good but this part is new to me.
Show more

The answer should be E. Both 10 and 52 fulfill the conditions in statements (1) and (2).
User avatar
EvaJager
User avatar
Joined: 22 Mar 2011
Last visit: 31 Aug 2016
Posts: 514
Own Kudos:
2,326
 [2]
Given Kudos: 43
WE:Science (Education)
Posts: 514
Kudos: 2,326
 [2]
What is my age (expressed as a positive integer)? Although 26 Feb 2014, 07:37
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EvaJager
aah123
Thanks Evajager,
Yes I did not consider 10, I don't know how come I counted only till 9.
So what's the answer then...is it (E) or (C).

I am just understanding how data sufficiency works, as my math concepts are good but this part is new to me.

The answer should be E. Both 10 and 52 fulfill the conditions in statements (1) and (2).
Show more

But taking into account the given piece of information that Although not young anymore, my age is still a two digit integer.,
only 52 is an answer.

Therefore, C and not E.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 Nov 2025
Posts: 105,414
Own Kudos:
778,486
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,414
Kudos: 778,486
What is my age (expressed as a positive integer)? Although 26 Feb 2014, 07:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EvaJager
EvaJager
aah123
Thanks Evajager,
Yes I did not consider 10, I don't know how come I counted only till 9.
So what's the answer then...is it (E) or (C).

I am just understanding how data sufficiency works, as my math concepts are good but this part is new to me.

The answer should be E. Both 10 and 52 fulfill the conditions in statements (1) and (2).

But taking into account the given piece of information that Although not young anymore, my age is still a two digit integer.,
only 52 is an answer.

Therefore, C and not E.
Show more

Very nice to see you back, Eva! Looking forward to your beautiful questions and solutions!
User avatar
stne
User avatar
Joined: 27 May 2012
Last visit: 20 Nov 2025
Posts: 1,770
Own Kudos:
1,974
Given Kudos: 658
Posts: 1,770
Kudos: 1,974
What is my age (expressed as a positive integer)? Although 26 Feb 2014, 07:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EvaJager
EvaJager
aah123
Thanks Evajager,
Yes I did not consider 10, I don't know how come I counted only till 9.
So what's the answer then...is it (E) or (C).

I am just understanding how data sufficiency works, as my math concepts are good but this part is new to me.

The answer should be E. Both 10 and 52 fulfill the conditions in statements (1) and (2).

But taking into account the given piece of information that Although not young anymore, my age is still a two digit integer.,
only 52 is an answer.

Therefore, C and not E.
Show more

Eva thanks for clearing that up !
User avatar
thefibonacci
User avatar
Joined: 22 Jan 2014
Last visit: 30 Jan 2019
Posts: 130
Own Kudos:
265
Given Kudos: 212
WE:Project Management (Computer Hardware)
Posts: 130
Kudos: 265
What is my age (expressed as a positive integer)? Although Updated on: 26 Feb 2014, 14:16
Originally posted by thefibonacci on 26 Feb 2014, 11:36.
Last edited by thefibonacci on 26 Feb 2014, 14:16, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EvaJager
I know my age is no excuse for the silly mistakes I am making sometimes. I cannot change my age, so I should do something about the mistakes...
Contemplating my age, I just realized that the integer number that represents my age has some very nice properties :o)

What is my age (expressed as a positive integer)? Although not young anymore, my age is still a two digit integer.

(1) My age is the sum of two distinct perfect squares.
(2) My age can be written as the product of a two digit integer and the sum of its digits. The two digits are distinct and their sum is a perfect square.
Show more

EvaJager is 52. ;)

Answer would be E.

1) a lot of options...so not sufficient.

2) sum of digits of any 2 digit number can be at max = 18.
so, we need to consider squares < 18 ie 1,4,9 and 16.
let the age be ab
=> (10a+b)(a+b) = age.
where a+b = perfect square.

for a+b=1 ; ab=10
for a+b=4 ; ab = 13 and 31 (since digits are distinct)
for a+b=9 ; ab = 18,27,... (but we can ignore 9 and 16 coz as soon as we multiply the sum of digits with the number, it would become a 3 digit number)

we are left with:
10*1 = 10
13*4 = 52
31*4 = a three digit number (ignore)

so, B alone is insufficient.

combine both statements.

age is a sum of 2 distinct prfct sq. and age can either be 10 or 52.
10 = 1^2 + 3^2
52 = 6^2+4^2

hence, the age can be 52 or 10. So E.
User avatar
EvaJager
User avatar
Joined: 22 Mar 2011
Last visit: 31 Aug 2016
Posts: 514
Own Kudos:
2,326
 [1]
Given Kudos: 43
WE:Science (Education)
Posts: 514
Kudos: 2,326
 [1]
What is my age (expressed as a positive integer)? Although 26 Feb 2014, 12:20
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
thefibonacci
EvaJager
I know my age is no excuse for the silly mistakes I am making sometimes. I cannot change my age, so I should do something about the mistakes...
Contemplating my age, I just realized that the integer number that represents my age has some very nice properties :o)

What is my age (expressed as a positive integer)? Although not young anymore, my age is still a two digit integer.

(1) My age is the sum of two distinct perfect squares.
(2) My age can be written as the product of a two digit integer and the sum of its digits. The two digits are distinct and their sum is a perfect square.

EvaJager is 52. ;)

Answer would be C.

1) a lot of options...so not sufficient.

2) sum of digits of any 2 digit number can be at max = 18.
so, we need to consider squares < 18 ie 1,4,9 and 16.
let the age be ab
=> (10a+b)(a+b) = age.
where a+b = perfect square.

for a+b=1 ; ab=10
for a+b=4 ; ab = 13 and 31 (since digits are distinct)
for a+b=9 ; ab = 18,27,... (but we can ignore 9 and 16 coz as soon as we multiply the sum of digits with the number, it would become a 3 digit number)

we are left with:
10*1 = 10
13*4 = 52
31*4 = a three digit number (ignore)

so, B alone is insufficient.

combine both statements.

age is a sum of 2 distinct prfct sq. and age can either be 10 or 52.
10 cannot be expressed in the form of x^2+y^2
52 = 6^2+4^2

hence, the age is 52....which can be found by combining both the fact statements.
Show more


\(10=1^2+3^2\)
User avatar
thefibonacci
User avatar
Joined: 22 Jan 2014
Last visit: 30 Jan 2019
Posts: 130
Own Kudos:
265
Given Kudos: 212
WE:Project Management (Computer Hardware)
Posts: 130
Kudos: 265
What is my age (expressed as a positive integer)? Although 26 Feb 2014, 14:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EvaJager
thefibonacci
EvaJager
I know my age is no excuse for the silly mistakes I am making sometimes. I cannot change my age, so I should do something about the mistakes...
Contemplating my age, I just realized that the integer number that represents my age has some very nice properties :o)

What is my age (expressed as a positive integer)? Although not young anymore, my age is still a two digit integer.

(1) My age is the sum of two distinct perfect squares.
(2) My age can be written as the product of a two digit integer and the sum of its digits. The two digits are distinct and their sum is a perfect square.

EvaJager is 52. ;)

Answer would be C.

1) a lot of options...so not sufficient.

2) sum of digits of any 2 digit number can be at max = 18.
so, we need to consider squares < 18 ie 1,4,9 and 16.
let the age be ab
=> (10a+b)(a+b) = age.
where a+b = perfect square.

for a+b=1 ; ab=10
for a+b=4 ; ab = 13 and 31 (since digits are distinct)
for a+b=9 ; ab = 18,27,... (but we can ignore 9 and 16 coz as soon as we multiply the sum of digits with the number, it would become a 3 digit number)

we are left with:
10*1 = 10
13*4 = 52
31*4 = a three digit number (ignore)

so, B alone is insufficient.

combine both statements.

age is a sum of 2 distinct prfct sq. and age can either be 10 or 52.
10 cannot be expressed in the form of x^2+y^2
52 = 6^2+4^2

hence, the age is 52....which can be found by combining both the fact statements.


\(10=1^2+3^2\)
Show more

missed that. damn. :cry:

thanks!!
Moderators:
Bunuel
Math Expert
105414 posts
kingbucky
496 posts